lecture02

lecture02 - 1 Distances (again) t(s) 0 v 30 Give two...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Distances (again) Example 1.1. Speedometer readings for a motorcycle at 12 second intervals are given: t ( s ) 0 12 24 36 48 60 v 30 28 25 22 24 27 Give two different estimates. 2 Definite Integral Recall what we just did. Definition 1. If f is a continuous function defined for a x b , we divide the interval [ a, b ] into n subintervals of equal width Δ x = ( b - a ) /n . We let x 0 = 1 , x 1 , . . . , x n = b be the endpoints of the intervals and we let x * 1 , x * 2 , . . . , x * n be any sample points in these intervals, so x * i is in [ x i - 1 , x i ]. The definite integral of f from a to b is Z b a f ( x ) dx = lim n →∞ n X i =1 f ( x * i x To make things easier, we usually pick the same point in every interval, usually either the left endpoint or the right endpoint. So usually x * i = x i or x * i = x i - 1 . Also, as long as f is continuous, it doesn’t matter which one we pick. They’ll always end up the same. Definition 2. In R b a f ( x ) dx , the f ( x ) is called the integrand. The a and b are limits of integration - a is the lower limit and b is the upper limit. dx has no official meaning by itself. It’s pretty much just a symbol.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

lecture02 - 1 Distances (again) t(s) 0 v 30 Give two...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online